1. Sign in to youtube
2. Go to www.youtube.com/html5(preview)
3. Click Join HTML5 trial
4. Make sure you're using the desktop version of youtbe (at the bottom of the page there's a link that says desktop).

On the youtube homepage there'll still be the download flash warning, but when looking at a video it should automatically open in the video player (if there's a html5 version, cause not all videos have been converted).